AUSTIN — The Texas Legislature's two chambers, both Republican-controlled but different in outlook, began this session's budget tussle Tuesday by issuing conflicting signals.

While both initial budget drafts covered the $2.7 billion cost of surging enrollment in Texas public schools, the Senate GOP leadership's version left $1.3 billion in available funds unspent and cut non-school spending by 1.5 percent across the board.

House Republican chiefs' version, meanwhile, spent $4 billion more in general-purpose state revenue than Comptroller Glenn Hegar said last week would be available.

That allowed them to add $1.5 billion for schools — contingent on passage of school finance fixes — and $162 million for mental health programs. Both are top priorities of House Speaker Joe Straus, R-San Antonio.

The Senate proposed continuing to spend $800 million on enhanced law enforcement at the Texas-Mexico border. The House would cut that to $663 million in 2018-19.

While Department of Public Safety director Steve McCraw asked for $300 million more, the ascension of President-elect Donald Trump — who vowed to build a border wall and get tough on federal immigration enforcement — appears to have given Texas GOP leaders cover to ignore McCraw's request. But at least for now, they don't feel comfortable redirecting the $800 million, even in a tight budget session.

In higher education, the House proposed spending $14.9 billion in general-purpose revenue, compared with the Senate's $14 billion.

Medicaid, the main safety net health care program, would receive nearly $2 billion less in state money from the Senate than from the House. One key difference is the Senate, in writing the next budget, would ignore a $1.2 billion Medicaid shortfall in the current cycle. The House assumed it is paid, as it usually is, and rolled that into the next cycle's presumed price tag.

Both chambers' first stabs at a two-year budget proposed continuing the new hires and pay raises approved last month for Texas' beleaguered Child Protective Services agency.

However, neither added any of the extra hundreds of millions that CPS and its parent department requested to make other improvements, including to foster care, which a federal judge has severely criticized in a case the state is losing.

"We keep overall spending low while making investments in children and our future," Straus said.

He touted the House version's higher spending on mental health, CPS and public schools. Straus predicted a final budget that "will put more dollars in the classroom, protect children and keep this state on sound fiscal footing."

Patrick noted that maintaining border security spending at $800 million would "allow for an additional 250 troopers by the end of the 2018-19 biennium."

"This budget is well within the available revenue and upholds our commitment to continue to live within our means and not spend more than the growth of our population times inflation," he said.

Nelson, in a separate statement, spoke of a "need to prioritize" and said there will be "difficult decisions" ahead. She noted that the Senate's base budget incorporates 4 percent cuts offered by agencies to GOP leaders last year, as well as the 1.5 percent trim. (The latter exempts the Foundation School Program, the main way the state funds public schools.)

The House's plan to set proposed spending slightly above Hegar's initial revenue forecast is a challenge to fiscal hawks who've advocated tighter and tighter restrictions on state spending.

If history is any guide, the Republican comptroller may very well up his estimate and put a little more cash on the table before the session ends May 29. That alone might bring the House's base budget under his revenue projection, as the Texas Constitution requires.

If not, House leaders have said they're confident they can cut or find other ways to get under the mark.

In 2003 and 2011, the Legislature used various accounting gimmicks to soften cuts. By a two-thirds vote of each chamber, lawmakers could grab some of the rainy day fund's more than $10 billion for the next cycle.

For fiscal hawks, that's never popular. But months from now, after examining austerity options, it could be more palatable.